Starlight in front of Earth is blueshifted, starlight behind Earth is redshifted. And the horizon is the angle where there is neither blueshift nor redshift.
Did you calculate how much that blue/red shift should be due to earth's motion, or are you just suggesting that such a shift should be observable?
The red shift as measured by astronomers show far-away galaxies moving away very fast (68 km/s per megaparsec) away from our own galaxy due to the expansion of the universe, not as a result of earth's own motion. As far as I know there is no part of the observable universe where all stars are blue shifted because we are moving towards that part of the cosmos.